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# Physics Module for 2014 E.C.ESSLCE Exam

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@RoomySodium

## Questions and Answers

### What is the difference between scalars and vectors?

Scalars are physical quantities with only magnitude, while vectors have both magnitude and direction.

### How are vectors represented analytically?

Vectors are represented analytically by a letter with an arrow over its head or with bold face letter.

### Which method is used to represent vectors by drawing a straight line with an arrow to scale?

• Scalar method
• Geometrical method (correct)
• Algebraic method
• Analytical method
• ### Vector addition is not simple algebraic addition, it obeys the laws of vector addition. The resultant of two vectors having the same direction is the ________ of the two vectors.

<p>algebraic sum</p> Signup and view all the answers

### How is the direction of the resultant vector determined when two vectors act at right angles to each other?

<p>The direction is determined using trigonometry, typically by finding the arctan of the ratio of the magnitudes of the two vectors.</p> Signup and view all the answers

### What are the types of forces according to Chapter Four: Dynamics? (Select all that apply)

<p>Applied force</p> Signup and view all the answers

### Angular position, angular velocity, and angular acceleration are topics covered in which chapter?

<p>True</p> Signup and view all the answers

### What is the type of motion discussed in Chapter Six?

<p>Oscillatory motion</p> Signup and view all the answers

### ______ is the law discussed in Chapter Eight related to electric charges.

<p>Coulomb Law</p> Signup and view all the answers

### Match the following topics with the correct chapter in the physics module:

<p>Work, energy, and power = Chapter Five Electrostatics and Magnetism = Chapter Eight Electric current and Magnetism = Chapter Nine Electromagnetic Induction and AC current = Chapter Ten</p> Signup and view all the answers

### What is the equation representing angular momentum according to Eqn. 3.6?

<p>$L = I\omega$</p> Signup and view all the answers

### What does Eqn. 3.7 represent?

<p>$I_i \omega_i = I_f \omega_f$</p> Signup and view all the answers

### What is the condition for two or more vectors to be equal?

<p>The same physical quantities, have the same magnitude, and have the same direction.</p> Signup and view all the answers

### What are the units for the gravitational constant G?

<p>N m² / kg²</p> Signup and view all the answers

### What is the formula for calculating the magnitude and direction of the car's resultant displacement?

<p>Magnitude = 39.0 km, Direction = 39.0 degrees west of north.</p> Signup and view all the answers

### In dynamics, what are the fundamental concepts that are described by Newton's laws of motion?

<p>All of the above</p> Signup and view all the answers

### What are the components of a vector in a three-dimensional space?

<p>Ax î + Ay ĵ + Az k̂</p> Signup and view all the answers

### What is a unit vector and how is it represented?

<p>A dimensionless vector with unit magnitude, represented as Â = A / |A|.</p> Signup and view all the answers

### Explain the scalar-vector multiplication and provide one rule associated with it.

<p>Scalar multiplication changes the magnitude but not the direction of a vector. One rule is that multiplying by 1 does not change the vector.</p> Signup and view all the answers

### What is the formula for the dot product of two vectors A and B?

<p>A · B = |A||B| cos(θ)</p> Signup and view all the answers

### What is the result of the cross product of vector A = (ax î + ay ĵ + az k̂) and vector B = (bx î + by ĵ + bz k̂)?

<p>(ay bz - az by) î + (az bx - ax bz) ĵ + ( ax by - ay bx) k̂</p> Signup and view all the answers

### What is the free-fall acceleration on the planet where an astronaut can jump a maximum horizontal distance of 15.0m with an initial speed of 3.00m/s?

<p>9.81 m/s^2</p> Signup and view all the answers

### What is the term used to describe the acceleration that is always toward the center of a circle, perpendicular to velocity?

<p>Centripetal acceleration</p> Signup and view all the answers

### What is the time taken for one complete rotation known as?

<p>Period (T)</p> Signup and view all the answers

### How is average angular velocity defined?

<p>Rate of change of the angular displacement of an object with respect to time</p> Signup and view all the answers

### What is the equation that describes the relationship for uniformly accelerated angular motion?

<p>ω = ωo + αt</p> Signup and view all the answers

### What quantity is expressed as a cross product of distance from the axis of rotation and linear momentum?

<p>Angular momentum (L)</p> Signup and view all the answers

### What does the moment of inertia of a body depend on?

<p>Size of the body, shape of the body, point of axis of rotation</p> Signup and view all the answers

### Define Torque.

<p>Rotational effect of force; Measure of force that causes an object to rotate around an axis.</p> Signup and view all the answers

### What factors does the magnitude of torque depend on?

<p>Size of force, moment arm of force, line of action of force</p> Signup and view all the answers

### What is the formula for calculating torque?

<p>τ = F rsin(θ)</p> Signup and view all the answers

### An electron in a cathode ray tube accelerates uniformly from 2.0 x 10^4 m/s to 6.0 x 10^6 m/s over 1.5 cm. How long does the electron take to travel this 1.5 cm?

<p>2.85 x 10^-8 s</p> Signup and view all the answers

### An electron in a cathode ray tube accelerates uniformly from 2.0 x 10^4 m/s to 6.0 x 10^6 m/s over 1.5 cm. What is its acceleration?

<p>1.40 x 10^14 m/s^2</p> Signup and view all the answers

### A track covers 40m in 8.5s while smoothly slowing down to a final speed of 2.8m/s. What is its original velocity?

<p>9.76 m/s</p> Signup and view all the answers

### A track covers 40m in 8.5s while smoothly slowing down to a final speed of 2.8m/s. What is its acceleration?

<p>-0.41 m/s^2</p> Signup and view all the answers

### A car traveling at a constant speed of 45m/s passes a trooper hidden behind a billboard. One second after the car passes, the trooper sets out to catch it at an acceleration of 3.0m/s^2. How long does it take for the trooper to overtake the car?

<p>15 s</p> Signup and view all the answers

### A jet lands on an aircraft at 140 mi/hr and stops in 2s due to an arresting cable. What is its acceleration?

<p>-31.06 mi/hr^2</p> Signup and view all the answers

### A jet lands on an aircraft at 140 mi/hr and stops in 2s due to an arresting cable. If the jet touches down at position xi = 0, what is the final position of the plane?

<p>140 mi</p> Signup and view all the answers

### A jet plane lands with a speed of 100 m/s and slows down at a rate of 5 m/s^2. What is the time interval needed for the jet to come to rest?

<p>20 s</p> Signup and view all the answers

### A jet plane lands with a speed of 100 m/s and slows down at a rate of 5 m/s^2. Can this jet land on an airport where the runway is 0.8 km long?

<p>No</p> Signup and view all the answers

### What is the mathematical expression of the restoring force dependent on?

<p>Specific physical system</p> Signup and view all the answers

### What is the defining property of linear momentum?

<p>Ability to cause change through motion</p> Signup and view all the answers

### Linear momentum is the product of mass of the system with its ________.

<p>velocity</p> Signup and view all the answers

### Linear momentum is a scalar quantity.

<p>False</p> Signup and view all the answers

### What is impulse defined as?

<p>Product of the force acting on an object and the time for which the force acts</p> Signup and view all the answers

### Match the following collision types with their descriptions:

<p>Elastic Collision = Collision type where both kinetic energy and momentum are conserved Inelastic Collision = Collision type where only momentum is conserved but kinetic energy is not conserved Perfectly Elastic Collision = Collision type where kinetic energy is fully conserved Perfectly Inelastic Collision = Collision type where colliding objects stick together after collision</p> Signup and view all the answers

### Which of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors?

<p>A ~ could be larger or smaller than AB, depending on the angle between the vectors</p> Signup and view all the answers

### Which of the following is equivalent to the scalar product: (A ~ × ~A) • ~B?

<p>(A ~ × ~A) • (B ~ × B)</p> Signup and view all the answers

### Which of the following statements is true about the relationship between the magnitude of the cross product of two vectors and the product of the magnitudes of the vectors?

<p>|A ~ × B| is smaller than AB</p> Signup and view all the answers

### Is the triple product defined by A • (B × C) a scalar or a vector quantity?

<p>Scalar</p> Signup and view all the answers

### What are the directions of (a) A × B and (b) B × A if vector A is in the negative y direction and vector B is in the negative x direction?

<p>(a) -k̂, (b) k̂</p> Signup and view all the answers

### Calculate the M • N, M × N, and the angle between M and N given M = 6î + 2ĵ - k̂ and N = 2î - ĵ - 3k̂.

<p>M • N = 8, M × N = -8î + 18ĵ - 10k̂, Angle between M and N = 98.13 degrees</p> Signup and view all the answers

## Study Notes

### Vectors

• Scalar quantities: physical quantities with only magnitude, e.g., electric charge, density, mass
• Vector quantities: physical quantities with both magnitude and direction, e.g., velocity, force, torque, electric field

### Vector Representation

• Analytical methods: represented by a letter with an arrow over its head or with bold face letter, e.g., →F or F, →P or P, →A or A
• Graphical/Geometrical methods: represented by a straight line with an arrow, where length is the magnitude and arrow direction is the direction

### Vector Addition and Subtraction

• Resultant vector (R): the sum of two or more vectors
• Vector subtraction: addition of the negative vector, e.g., →R = →A - →B = →A + (-→B)
• Vector addition laws:
• The resultant of two vectors with the same direction is the algebraic sum of the two vectors with the same direction as both.
• Not commutative: order of vectors matters, e.g., →A + →B ≠ →B + →A
• Associative: (→A + →B) + →C = →A + (→B + →C)

### Key Concepts

• Magnitude: the size or amount of a vector
• Direction: the orientation or direction of a vectorHere are the study notes for the text:

### Kinematics

• Definition: Kinematics is a branch of mechanics that describes the motion of an object without reference to the cause of motion (force).

### One or Two Dimensional (2D) Motion

• Motion: Continuous change of position with time.
• Position: Location of an object with respect to a chosen reference frame or point.
• Reference Frame: A system of graduated lines symbolically attached to a body that serves to describe the position of points relative to the body.

### Types of Motion

• Translational Motion: When all points of an object move the same distance in a given time.
• Rectilinear motion: Object moves in a straight line (e.g. car moving in a straight line, bullet being fired).
• Curvilinear motion: Object moves along a curved path (e.g. child going down a slide, bird flying in the sky).
• Rotational Motion: When an object moves about an axis and different parts of it move by different distances in a given interval of time.
• Examples: Blades of a rotating fan, merry-go-round, blades of a windmill.
• Vibrational Motion: When a body moves to and fro about its mean position.
• Examples: Pendulums, swings, tuning forks.

Let me know if this meets your requirements!### Vibrational Motion

• Vibrational motion can be periodic or non-periodic

### Kinematics of the Particle

#### Motion in 1D

• Motion of a particle along a straight line in a fixed direction (or motion along one coordinate axis)
• Example: a car moving along a flat straight narrow road

#### Kinematical Terms

• Distance: total path length covered by the moving object
• Displacement: change of position (shortest distance between start and end of motion)
• Speed: rate of change of distance in a unit time
• Average Speed: total distance traveled by the total time required to cover the distance
• Velocity: rate of change of displacement as a function of time
• Average Velocity: change of displacement divided by the time interval during which the displacement occurs
• Instantaneous Velocity: velocity of the particle at a given instant of time (limit of average velocity as Δt approaches to zero)
• Instantaneous Speed: magnitude of instantaneous velocity

#### Acceleration

• Acceleration: rate of change of velocity
• Average Acceleration: change in velocity divided by the time interval during which the change in velocity occurs
• Instantaneous Acceleration: acceleration of the particle at a given instant of time (limit of average acceleration as Δt approaches to zero)

#### Uniform Motion in 1D

• Uniform Motion: equal distances traveled in equal intervals of time
• Acceleration: zero
• Velocity: remains constant
• Speed: equal to the actual speed
• Instantaneous Velocity: equal to the actual velocity

#### Uniformly Accelerated Motion in 1D

• Uniformly Accelerated Motion: motion with constant acceleration
• Velocity: changes with uniform rate
• Equations of Motion:
• v(t) = vi + at
• ∆x = vi t + (1/2) at^2
• v^2 = vi^2 + 2a∆x

### Free Falling Bodies

• Free Falling Bodies: objects moving freely under the influence of gravity alone
• Equations of Motion:
• vy = gt
• ∆y = (1/2) gt^2
• vy^2 = 2g∆y

### Two-Dimensional Motion

• Two-Dimensional Motion: motion in a plane (two coordinate axes simultaneously)
• Displacement: ∆~r = ~rB - ~rA
• Average Velocity: ~vav = ∆~r / ∆t
• Instantaneous Velocity: v(t) = lim (∆~r / ∆t) as Δt approaches to zero
• Average Acceleration: ~aav = ∆~v / ∆t
• Instantaneous Acceleration: a(t) = lim (∆~v / ∆t) as Δt approaches to zero

### Projectile Motion

• Projectile Motion: motion of an object in a plane under the influence of gravity alone
• Trajectory: parabolic path
• Horizontal Motion: uniform motion (ax = 0)
• Vertical Motion: uniformly accelerated motion (ay = -g)
• Equations of Motion:
• x(t) = v0x t
• y(t) = v0y t - (1/2) gt^2
• v0y = v0 sinθ
• ymax = v0y^2 / 2g
• t = 2v0y / g
• R = v0^2 sin(2θ) / g

### Circular Motion

• Circular Motion: motion in a circular path at a constant speed
• Uniform Circular Motion: constant speed and direction
• Velocity: not constant due to continuous change in direction
• Acceleration: radial acceleration (a = v^2 / r)

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## Description

This quiz is a part of the Pre-University Remedial Program for the 2014 E.C.ESSLCE exam in Ethiopia, covering the Physics Module, specifically vectors and scalar quantities.

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